DE102005043010A1 - Decimating filter cascade with minimized settling time after reinitialization - Google Patents

Abstract

A filter cascade consists of at least one filter path (FP¶1¶; FP¶2¶) each with at least one decimating filter (F¶0¶, F¶1¶, F¶2¶, ..., F¶N-1¶ ). The input of the filter cascade is acted upon by a sampled input signal (X¶0¶ (k¶0¶)) with several valid signal sections separated from each other by at least one invalid sampling value. Each decimating filter (F¶0¶, F¶1¶, F¶2¶, ..., F¶N-1¶) is reinitialized at the beginning of a valid signal section and then generates the at the input after a minimum number of samples (E) the input signal present in the filter cascade (y¶0¶ (k¶0¶)) at the filter output (A¶0¶, A¶1¶, A¶2¶, ..., A¶N-1¶) steady sample value, whereby the minimum number of sample values corresponds to the filter length DOLLAR I1 of the respective filter path (FP¶1¶, FP¶2¶) reduced by a factor of 1.

Description

The The invention relates to a decimating filter cascade with minimized Settling time after reinitialization.

In There are many applications in digital signal processing in which the sampling frequency of the sampled signal is reduced must become. Decimating filters are used for this purpose divide into transversal and polyphase filters.

in eine Abtastfrequenz f_a,out seines Ausgangssignals durch. Über die Polyphasenkomponente p wird vom idealen Polyphasendezimator PPD der Phasenversatz des Ausgangssignals gegenüber dem Eingangssignal in Anzahl von Abtastzeitpunkten eingestellt. 2 zeigt für ein gegebenes Eingangssignal x_Dezimator(k) das von einem idealen Polyphasendezimator PPD erzeugte abtastratenreduzierte Ausgangssignal y_DEZIMATOR(l) für einen Dezimationsfaktor R = 3 und eine Polyphasenkomponente von p = 0, p = 1 und p = 2.Real polyphase filters, which will be considered below, can be described by an equivalent circuit with a series circuit of a non-decimating filter NDF and an ideal polyphase decimator PPD. According to 1 For example, the non-decimating filter NDF is implemented, for example, as a finite-impulse-response (FIR) filter with a transfer function h (k) and a filter length L. Alternatively, an infinite impulse response filter (IIR filter) or a cascaded integrator comb filter (CIC filter) can also be used for the non-decimating filter. The ideal polyphase decimator PPD connected in series leads to a reduction of the sampling frequency f _{a, in} its input signal by a decimation factor

in a sampling frequency f _{a, out of} its output signal. About the polyphase component p is set by the ideal Polyphasendezimator PPD, the phase offset of the output signal to the input signal in number of sampling times. 2 For a given input signal x _decimator (k), the sample rate reduced output signal y _DECIMATOR (l) generated by an ideal polyphase _decimator PPD is given for a decimation _factor R = 3 and a polyphase component of p = 0, p = 1 and p = 2.

The Filtering the sampled input signal in a FIR filter NDF causes the resulting output due to the convolution of the sampled Input signal with the impulse response h (k) of the FIR filter NDF first after a certain number of sampling times has a "correct value" and thus has settled. This transient is after total L - 1 Sampling times completed, where L is the filter length of FIR filters NDF is. By combining the FIR filter NDF with the ideal polyphase decoder PPD results, as below will be shown in detail, a further deterioration of the transient process.

In the spectrum analysis may be after a down-conversion from the intermediate frequency to baseband, receive filtering and a strong sample rate reduction the minimum bandwidth of the so-called VIDEO filter depends on The measurement may be, for example, 1 Hz, so that the sampling rate of the signal at the output of the filter cascade is correspondingly low. Especially at such low sample rates of the signal at the output of the filter cascade the measuring time can be shortened by an optimal choice of the polyphase component.

Come in addition, that in many measurement applications such as spectrum analysis so-called gated measurements are carried out in which several Signal sections with valid Measured values of Signal sections with invalid readings are interrupted. Each new signal section containing valid measured values represents for the decimating filter cascade is a new stimulus that leads to a new transient of the decimating filter cascade leads. in the Contrary to the first valid Signal section in which the decimating filter cascade beforehand no Suggestion by invalid readings learns becomes the decimating filter cascade in all subsequent valid signal sections in advance with invalid Measured values wrongly excited and at the time of insertion of the valid signal section in converts a filter state, the not the original filter condition at the beginning of the first valid Signal section corresponds and therefore to a further deterioration the settling time of the decimating filter cascade can lead.

task The invention is therefore the settling time of a decimating Filter cascade, especially for the application of gated Measurements, to minimize.

The The object is solved by the features of claim 1. The dependent claims contain advantageous developments of the invention.

When Condition for a minimized settling time of the decimating filter or The decimating filter cascade becomes the settling time of an FIR filter NDF, the number of sampling times of the output signal in height the reduced by a factor of 1 filter length L corresponds.

These it is a single decimating filter, according to the invention results in the polyphase component p of the ideal polyphase decimator PPD for a minimum settling time of the decimating filter as the remainder of the modulo division around the Factor 1 reduced filter length L by the decimation factor R. In such an occupancy of the Polyphase component p comes exactly one sample of the output signal of the decimating filter at the sampling instant of the input signal of the decimating filter by a total of L - 1 sampling times from the beginning of the excitation of the decimating filter and thus the earliest possible Time has settled.

Lies a decimating filter cascade, the invention results in the polyphase components the individual polyphase decimators PPD of the decimating filter cascade from the consideration that each exactly one sample of all samples of the voltage applied to the output of the respective Polyphasendezimators PPD Output signal to the sampling time of the input signal the decimating filter cascade comes to lie which by a number from sampling instants from the beginning of the decimating excitation Filter Cascade is located, which reduced exactly by a factor of 1 Filter length L the entire decimating filter cascade. In such a Determination of the polyphase component of all Polyphasendezimatoren PPD the decimating filter cascade are all according to the invention Output signals of the serially connected in the decimating filter cascade decimating filter as early as possible.

Besides a purely serial arrangement of the individual decimating filters in a decimating filter cascade, there are also applications of decimating filter cascades in which the individual decimating filters are arranged both serially and parallel to one another. Due to the serial and parallel connection of the individual decimating filters, there are several inputs E ₁ , E ₂ ,..., And outputs A ₁ , A ₂ ,..., And thus several filter paths between one input and one output in such a decimating filter cascade educated. In order to realize a minimal settling of each filter path of the decimating filter cascade, the individual polyphase components p of the individual decimating filters of the respective filter path must be designed analogously as in the case of a purely serial connection of the individual decimating filters in a decimating filter cascade.

Lies an input signal of the decimating filter cascade that several Signal sections with valid Having samples, each with a signal section with invalid Samples are separated from each other, the individual decimating Filter the decimating filter cascade at the beginning of each valid signal segment reinitialized. The reinitialization of decimating filters causes a reset of all delay stages the FIR, IIR, non-decimating filter component or CIC filter and the decimating filter portion used Polyphasendezimatoren.

The Reinitialization of each decimating filter can each be done over one Control signal done centrally by a higher-level unit for flow control is generated or upstream of the respective filter path decimating filter after its reinitialization passed becomes.

To the reinitialization of the decimating decimating filters Filter cascade are the polyphase components of the individual Polyphasendezimatoren equivalent to dimension as with an input signal containing only valid samples, to a settling of the decimating filter cascade in minimal To ensure time.

embodiments the decimating invention Filter cascade are below taking into account the drawing explained in more detail. In show the drawing:

1 an equivalent circuit for a decimating filter,

2 a timing diagram of the input and output of an ideal Polyphasendezimators for different polyphase components p,

3 3 is a timing diagram of the input, intermediate and output signals of a decimating filter according to the prior art and of a decimating filter according to the invention without reinitialization.

4 an equivalent circuit diagram of a first embodiment of a decimating filter cascade without reinitialization,

5 a time diagram of the input, intermediate and output signals of a decimating filter cascade according to the invention without reinitialization,

6 an equivalent circuit diagram of a second embodiment of a decimating filter cascade without reinitialization,

7 a timing diagram of a gated input signal, the corresponding FIR filter output signal and the corresponding Polyphasendezimator-output signal of the decimating filter according to the invention without reinitialization and reinitialization,

8th a time diagram of a gated input signal of the corresponding first polyphase and the second polyphase output signal of the decimating filter cascade according to the invention with reinitialization,

9 a block diagram of a first embodiment of a decimating filter cascade according to the invention with Reinitialisierung and

10 a block diagram of a second embodiment of a filter cascade according to the invention with reinitialization.

Based on the timing diagrams of 3 In the following, the relationships for the interpretation of a fiction, contemporary decimating filter with minimal settling time without reinitialization will be explained.

The decimating filter is according to 1 and 3 , Line 1, at its input E with a sampled input signal x _decimation filter (k) applied, which is also the input signal x _FIR (k) of the non-decimating FIR filter NDF. The FIR filter NDF has a filter length L of 6 such that the sampled output signal y _FIR (k), which is simultaneously the sampled input signal x _decimator (k) of the ideal polyphase decoder PPD, after a total of L - 1 = 5 sampling times since excitation of the FIR filter NDF with the sampled input signal x _FIR (k). The steady state of the sampled output signal y _FIR (k) of the FIR filter NDF for sampling times k ≥ L-1 = 5 is in 3 Line 2 is indicated by a filled-in sample, while the non-steady state samples y _FIR (k) of the output signal of the FIR filter NDF for sampling times k <L-1 = 5 are represented by an unfilled sample.

The output signal y _decimator (I) of the ideal polyphase _decimator PPD, whose running index I indicates the reduced sampling rate f _{a, out} , is at the same time also the output signal y _decimation filter (l) of the decimating filter. The ideal Polyphasendezimator PPD generated from its sampled input signal x _decimator (l) according to equation (1) by means of the adjustable polyphase component p and the adjustable decimation factor R a sampling rate reduced output signal y _decimator (l). y decimator (l) = x decimator (l * R + p) (1)

The setting of the decimation factor R results, as already shown above, the amount of sampling rate reduction between the sampling rate f _{a, in} the input signal x _decimator (l) and the sampling rate f _{a, out of} the output signal y _decimator (l).

The setting of the polyphase p, which is carried out according to the condition in equation (2), determines at what point the sampled output signal y _decimator (l) relative to the sampled input signal x _decimator (l) is produced: 0 ≤ p ≤ R - 1 (2)

The l-th sample of the output signal y _decimator (l) appears at given decimation factor R and given polyphase component p to the sampling instant k calculated according to equation (3) at the output of the ideal polyphase decimator PPD. k = l * R + p (3)

If the decimation factor R = 4 and the polyphase component p = 0 are selected for a non-optimized transient response of the decimating filter, the first steady state value of the sampled output signal y _decimator (l) of the ideal polyphase decoder PPD appears at the instant k = 8 (FIG. 3 , Line 3). With an optimum choice of the polyphase component p = 1, a steady-state output value is already obtained at k = 5 at the output of the ideal polyphase decimator PPD ( 3 , Line 4). This corresponds to the minimum settling time of the FIR filter NDF determined by the filter length L = 6 of the FIR filter NDF.

As an optimality criterion, the condition in equation (4) must therefore be satisfied on the basis of equation (3). k = L-1 = l * R + p (4)

This optimality criterion for minimized transient response of a decimating filter implies the calculation rule for the polyphase component P shown in equation (5): p = MOD {L-1, R} (5)

Thus, at the earliest possible time k = L-1, a steady-state output value is obtained at the output A of the decimating filter. For an IIR or CIC filter, the corresponding system-theoretical replacement filter length L ~ _IIR or L ~ _{CIC is used} instead of the filter length L in equation (3).

Starting from equation (2), the time gain .DELTA.t with optimum selection of the polyphase component P is compared to the worst case choice of the polyphase component P according to equation (6):

If the signal processing chain consists not only of a single decimating filter, but of several decimating filters connected in series in accordance with the first embodiment of the invention, then the polyphase component p adjustment parameter of equation (5) must be the ideal polyphase decoder PPD for the optimum polyphase component adjustment p _{i of} the individual polyphase decimators PPD _{i of} the filter cascade are expanded, as will be deduced below.

According to 4 the decimating filter cascade consists of a total of N decimating filters F ₀ , F ₁ , F ₂ , ..., F _N-1 , each of which - without the in 1 represented conceptual separation into a non-decimating FIR filter NDF and an ideal Polyphasendezimator PPD - a transfer function h _i (k _i ), a filter length L _i , a decimation factor R _i and a polyphase component p _i have. The decimating filter F _i generates an output signal y _i (k _j ) whose index k _j corresponds to the sampling rate f _{a, j} from an input signal x _i (k _i ) whose index k _{i is} higher than the sampling rate f _{a, j} Sample rate f _{a, i} corresponds. For a non-decimating filter NDF, R _i = 1 and p _i = 0 apply in this notation.

The decimating filters F _i , ..., F _j-1 between the levels i and j - in 4 If i = 0 and j = 3 are selected, they can be replaced by a decimating replacement filter with the transfer function h _ij (k _i ), the filter length L _ij , the decimation factor R _ij and the polyphase component p _ij . The substitutes h ~ _ij (k _i ), L ~ _ij , R ~ _ij and p ~ _{ij are} calculated as follows:
For the decimation factor R ~ _{ij of} the decimating replacement filter, the calculation rule in equation (7) applies, where R _{ξ is} the decimation factor of the decimating filter F _ξ :

For the polyphase component p ~ _{ij of} the decimating replacement filter, the calculation rule in equation (8) applies, where p _{ξ is} the polyphase component of the decimating filter F _ξ :

In order to calculate the replacement transfer function h ~ _ij (k _i ), first the individual transfer functions h _ξ (k _ξ ) of the respective decimating filter F _ξ between the scanning planes i <ξ <j from the plane ξ with the sampling frequency f _{a, ξ} in the plane i with the sampling frequency f _{a, i to be} transformed. A transfer function transformed to the plane i with the sampling frequency f _{a, i} is referred to below as h ~ _ξ (k _i ) and has the property according to equation (9):

The transformed transfer function h ~ _ξ (k _i ) of the decimating filter F _ξ results from the original transfer function h _ξ (k _ξ ) of the decimating filter F _ξ , by the transformed transfer function h ~ _ξ (k _i ) between the individual sampling times k _i = R ~ _iξ · k _ξ is supplemented with a total of R ~ _iξ - 1 zeros.

Thus, the transfer function h ~ yields according to equation (10) _ij (k _i) of the decimating replacement filter between the scanning planes i and j of a convolution of the scan region i transformed transfer functions h ~ _ξ (k _ξ) of the individual decimating filter F _ξ between the scanning planes i <ξ <j: h ~ ij = h i (k i ) · H ~ i + 1 (k i ) · ... · h ~ j-2 (k j-2 ) · H ~ j-1 (k j-1 ) (10)

The length L ~ _{ij of} the substitute filter is obtained according to equation (11) from the filter length L _{ξ of} the decimating filter F _ξ and the decimation _factor R _{iξ of} the decimating substitute filter between the sampling plane i and ξ:

The temporal relationship between the scanning region i and the scanning region j is based on equation (3) according to equation (12): k i = k j · R ~ ij + p ~ ij (12)

Analogous to the minimum settling time of a single decimating filter F _ξ in the amount of reduced by the factor 1 filter length L of the FIR filter NDF results in the minimum settling time of a decimating filter cascade with several decimating filters F _i , ..., F _j-1 between the Scanning planes i and j from the reduced by a factor of 1 filter length L ~ _ij the replacement filter between the scan planes i and j. Consequently, according to equation (13), considering equation (11) at the sampling time k _i, a sample must be present at the output A _i , ..., A _{j-1 of} the decimating filter cascade F _i , ..., F _j-1 to achieve a minimal settling of the decimating filter cascade.

The time gain .DELTA.t with optimum selection of the polyphase components of a decimating filter cascade in comparison to the worst-case choice of the polyphase components of a decimating filter cascade is according to equation (14):

Analogous to the optimality criterion for minimized transient response of a decimating filter in equation (5), for each decimating filter F _{ξ of} a decimating filter cascade between the sampling planes i and j, a sample in the sampling plane F _ξ at the sampling time k _ξ at the output of the decimating filter F _{ξ must be} present y _ξ-1 (k _ξ ) of the output signal y _ξ-1 at the sampling time k _i = L ~ _ij - 1 come to lie in the scanning plane i. Starting from equation (12), in analogy to equation (12), in the case of a single decimating filter, the optimality criterion in equation (15) must be satisfied. k i = L ~ ij - 1 = k ξ · R ~ iξ + p ~ iξ ∀i <ξ ≤ j (15)

This optimality criterion for minimized transient response of a decimating filter cascade implies that the sampling instant k _ξ of the sampling value y _ξ-1 (k _ξ ) of the output signal y _{ξ-1 present} at the output of each decimating filter F _ξ must be an integer and thus satisfy equation (16) : MOD {k i - p ~ iξ , R ~ iξ } = 0 ∀i <ξ ≤ j (16)

The optimality criterion in equation (16) can be reshaped as follows:
For this purpose, equation (8) is mathematically transformed according to equation (17):

Applying the knowledge from equation (17) in the optimality criterion of equation (16), equation (18) results: MOD {k i - p ~ i, ξ-1 - R ~ i, ξ-1 p ξ-1 , R ~ iξ } = 0 ∀i <ξ ≤ j (18)

For simplicity, equation (18) is rewritten into an equivalent form according to equation (19): MOD {A - bC, R} = 0 with A = k i - p ~ i, ξ-1 ; b = R ~ i, ξ-1 ; C = p ξ-1 ; R = R ~ iξ (19)

Equation (19) can be converted to equation (20) or equation (21) by introducing an integer factor λ: A - bC - λR = 0 (20) C = 1 b (A - λ R) (21)

The right-hand side of equation (21) can again be described as a modulo condition according to equation (22): C = 1 b · MOD {A, R} (22)

If a substitution of the auxiliary quantities A, b, C and R from equation (19) is carried out in equation (22), equation (23) is obtained:

Substitution of μ = ξ - 1 in equation (23) gives equation (24):

By means of equation (24), the individual polyphase factors p _{μ of} the individual decimating filters F _{μ of} the decimating filter cascade can be calculated iteratively starting with μ = i.

A decimating filter cascade of, for example, three decimating filters is given. At time k ₀ = L ~ ₀₃ - 1, a decimating filter cascade should have settled. The individual polyphase components p ₀ ,..., P _{2 of} the three decimating filters can be determined according to Equations (24a), (24b) and (24c):

The timing diagram in 5 shows for a first embodiment of a decimating filter cascade of two serially connected decimating filters in line 1 a sampled input signal x ₀ (k ₀ ), in line 2 the sampled output signal y ₀ (k ₁ ) at the output of the first decimating filter and in line 3 the sampled output signal y ₁ (k ₂ ) at the output of the second decimating filter.

In 5 It can be seen that in line 2 with the selection of the polyphase component p _{0 of} the first decimating filter F ₀ (p ₀ = 1) according to equation (24a) (p ₀ = MOD {k ₀ = L ₀ -1, R ₀ } = MOD {4, 3}) a time-optimal settling of the first decimating filter F ₀ at the sampling time k ₀ = L ₀ -1 = 4 is achieved.

ebenfalls ein zeitoptimales Einschwingen des zweiten dezimierenden Filters F₁ zum Abtastzeitpunkt k₀ = L ~₀₂ – 1 = 10 gemäß Gleichung (12) bei einer Filterlänge L ~₀₂ = 11 der dezimierenden Filterkaskade gemäß Gleichung (11) erreicht wird.From line 3 of the 5 will also be recognized that with the choice of polyphase p ₁ of the second decimating filter F ₁ (p ₁ = 1) in accordance with equation (24b)

also a time optimal settling of the second decimating filter F ₁ at the sampling time k ₀ = L ~ ₀₂ - 1 = 10 according to equation (12) at a filter length L ~ ₀₂ = 11 of the decimating filter cascade according to equation (11) is achieved.

In a second embodiment of a filter cascade according to the invention according to 6 the individual decimating filters are not only serial, but also connected in parallel. For example, forms in the decimating filter cascade of 6 in this way, between the input E and a first output A _{1 of} the decimating filter cascade, a first filter path FP ₁ with the decimating filter F ₀ and the decimating filter F ₁ serially connected thereto and a second filter path FP ₂ with the decimating filter F ₀ and the decimating filter F ₂ .

For the determination of optimized polyphase components in the individual decimating filters F ₀ , F ₁ , F ₂ , the individual filter paths FP ₁ , FP _{2 are to be} regarded as a serial connection of several decimating filters F ₀ , F ₁ , F ₂ and in an analogous manner as in FIG to proceed first embodiment of a decimating filter cascade according to the invention. In this way, it can be ensured in particular that output signals are generated at the same times in both filter paths FP ₁ , FP ₂ .

Will a single decimating filter match 1 with a sampled input signal x _{decimation filter} (k) = x _FIR (k) according to 7 . 1 , Line applied to signal sections with valid samples - filled samples in 7 And intermediate signal sections with invalid samples - unfilled samples in 7 - exists, so are due to the convolution of the input signal x _decimation (k) = x _FIR (k) with the impulse response h (k) of the non-decimating filter NDF, according to 1 is realized as an FIR filter, at the output of the FIR filter only after a total of L - 1 sampling times from the beginning of a valid signal portion of the input signal x _decimation filter (k) = x _FIR (k) valid samples of the output signal y _FIR (k) = x _decimator (k) before. Since the filter length L in the FIR filter of 7 has the value 6 and the first valid signal section at the sampling time k = 0 and the second valid signal section at the sampling time k = 13 begins, are at the output of the FIR filter according to 7 . 2 , Line, only at the time k = 5 or at the sampling time k = 18 valid samples of the output signal y _FIR (k) = x _decimator (k) before.

The sampled signal y _decimator (I) at the output A of the polyphase _decimator PPD has at a decimation factor R = 4 and a polyphase component p = 1 in the absence of reinitialization of the FIR filter in 7 . 3 , Line, displayed history. It can be seen that in the first valid signal section of the input signal x _decimation filter (k) = x _FIR (k) the sampled output signal y _decimator (l) of the decimating filter at the sampling time k = 5 at the minimum settling time valid samples, while in the second valid signal section of the input signal x _decimation filter (k) = x _FIR (k) the sampled output signal y _decimator (l) of the decimating filter only at the sampling time k = 21 and not at the earliest possible sampling instant k = 18 valid samples. This degraded settling of the decimating filter in the second signal section results from the non-original filter state of the non-decimating FIR filter and the polyphase decimator described above in the introduction at time k = 13 of the beginning of the second valid signal section.

If, on the other hand, the decimating filter-not decimating FIR filter and polyphase decimator-is reset according to the invention at the beginning of each signal section having valid samples of the input signal x _decimation filter (k) = x _FIR (k), then the polyphase component p of the polyphase decimator is optimally adjusted PPD a settling of the decimating filter in minimal time. A reset - reinitialization - of the decimating filter at the beginning of the first signal section is not required because at this time the decimating filter is in its original filter state.

In the 4th line of the 7 the optimum settling of the sampled output signal y _decimator (l) of the decimating filter in the second valid signal section upon reinitialization of the decimating filter at the sampling instant k = 13 of the beginning of the second valid signal section can be seen: At minimum settling time the decimating filter is earliest possible at the sampling time k = 18 settled at its output A.

In the time diagram of 8th is the settling of a decimating filter cascade according to the invention with two decimating filters connected in series with a sampled input signal x _decimation filter (k) = x _FIR (k) with a start of a valid signal section at the sampling time k = 0 and k = 14 ( 8th . 1 , Line). The first decimating filter with a filter length L ₀ = 5 oscillates at a decimation factor R ₀ = 3 and an optimized polyphase component p ₀ = 1 in the first valid signal section at the earliest possible sampling time k = L ₀ -1 = 4 and in the second valid signal section at a reinitialization of the decimating filter at time k = 14 of the beginning of the second valid signal section at the earliest possible sampling time k = 14 + L ₀ -1 = 18 ( 8th . 2 , Row). Analogously, the second decimating filter with a filter length L ₁ = 3 oscillates at a decimation factor R ₁ = 2 and an optimized polyphase component p ₁ = 1 in the first valid signal segment at the earliest possible sampling time k = L ~ ₀₂ - 1 = 10 with a replacement filter length L ~ ₀₂ = 11 of the decimating filter cascade and in the second valid signal section upon reinitialization of the decimating filter at time k = 14 of the beginning of the second valid signal section at the earliest possible sampling instant k = 14 + L ~ ₀₂ - 1 = 24 ( 8th . 3 , Row). The time interval between the last and the next sample value can be left unchanged by the reinitialization, but it can also be shortened (2 sampling times k ₀ in the signal y ₀ (k ₁ ) of the line 2 of FIG 8th ) or extend (8 sampling times k ₀ in signal y ₁ (k ₂ ) of line 3 of FIG 8th ).

Reinitialization of the individual decimating filters of a decimating filter cascade according to the invention takes place in a first embodiment of the filter cascade according to the invention with reinitialization in 9 centrally via a unit to the higher-level sequence control EAS, which, starting from the sampled input signal x _decimation filter (k) = x _FIR (k) of the decimating filter cascade for each decimating filter F ₀ , F ₁ , F ₂ , ..., F _N-1 Reinitialisierungssignal R for resetting all the delay stages of the respective non-decimating FIR filter and the Polyphasendezimators each decimating filter F ₀ , F ₁ , F ₂ , ..., F _N-1 generated. The respective reinitialization signal R is represented by a delay element VZ ₀ , VZ ₁ , VZ ₂ ,... Integrated in the respective path from the unit to the superordinate sequence control EAS to the respective decimating filter F ₀ , F ₁ , F ₂ ,..., F _n-1 . .., VZ _N-1 each with a specific delay time T ₀ , T ₁ , T ₂ , ..., T _N-1 delayed. This specific delay time T ₀ , T ₁ , T ₂ ,..., T _N-1 takes into account the different hardware-related transit time of the measurement signal to be filtered from the input of the filter cascade to the input of the respective filter F ₀ , F ₁ , F ₂ ,. ., F _N-1 and thus causes a time-correct reset of the respective filter F ₀ , F ₁ , F ₂ , ..., F _N-1 .

In a second embodiment of the filter cascade according to the invention with reinitialization in 10 the reinitialization signal R is generated without delay by a unit for the higher-level sequence control EAS starting from the sampled input signal x _decimation filter (k) = x _FIR (k) of the decimating filter cascade and fed to the first decimating filter F ₀ for resetting all delay stages. This first decimating filter F ₀ passes the Reinitialisierungssignal R directly - only by the hardware-related delay time - to the second decimating filter F ₁ for resetting its delay stages on. In this way, the reinitialization signal R is passed from each upstream decimating filter to the respective subsequent decimating filter until it has arrived at the last decimating filter F _N-1 .

The reinitialization of the filter states of the non-decimating filter and of the polyphase decimator shown hitherto can alternatively also be based on a reinitialization of only the filter states of the polyphase decimators be limited. Although the signal values at the output of the filters in the phase of the transient process are different from the signal values at the output of the filters in the phase of the transient during the reinitialization described in such Reinitialisierung, the settling time is equivalent in both cases equivalent minimal.

The invention is not limited to the illustrated embodiments. In particular, except in 6 filter structure shown, other filter structures of a decimating filter cascade covered by the invention. If there are variably programmable filter lengths of the individual decimating filters, a freely programmable calculation of the individual polyphase components is likewise covered by the invention.

Claims (10)

Filter cascade with at least one filter path (FP ₁ , FP ₂ ) each consisting of at least one decimating filter (F ₀ , F ₁ , F ₂ , ..., F _N-1 ), wherein the input (E) of the filter cascade of a sampled Input signal (x ₀ (k ₀ )) is applied to a plurality of valid signal sections separated by at least one invalid sample, characterized in that each decimating filter (F ₀ , F ₁ , F ₂ , ..., F _n-1 ) respectively is reinitialized at the beginning of a valid signal section and then after a minimum number of sampling values of the input signal (x ₀ (k ₀ )) present at the input (E) of the filter cascade at the filter output (A ₀ , A ₁ , A ₂ ,. A _N-1 ) generates a steady-state sample, the minimum number of samples corresponding to the filter length L ~ of the respective filter path (FP ₁ , FP ₂ ) reduced by the factor 1. Filter cascade according to Claim 1, characterized in that each decimating filter (F ₀ , F ₁ , F ₂ , ..., F _N-1 ) via an associated control signal from a higher-level control unit (EAS) at the beginning of a new valid signal section is reinitialized. Filter cascade according to Claim 1, characterized in that each decimating filter (F ₁ , F ₂ , ..., F _N-1 ) is separated from its upstream decimating filter (F ₀ , F ₁ , F ₂ , ..., F _{N-). 2} ) is reinitialized via a control signal after its reinitialization at the beginning of a new valid signal section. Filter cascade according to one of Claims 1 to 3, characterized in that, after reinitialization of each decimating filter (F ₀ , F ₁ , F ₂ , ..., F _N-1 ), the generation of the first sample at the respective filter output (A ₀ , A ₁ , A ₂ , ..., A _N-1 ) is instantaneous. Filter cascade according to one of Claims 1 to 4, characterized in that the respective decimating filter (F ₀ , F ₁ , F ₂ , ..., F _N-1 ) consists of a non-decimating filter (NDF) in series with a polyphase decimator ( PPD). Filter cascade according to claim 5, characterized in that that this non decimating filters (NDF), a finite impulse response filter, an infinite impulse response filter or a cascaded integrator comb filter is. Filter cascade according to Claim 5 or 6, characterized in that the reinitialization of the respective decimating filter (F ₀ , F ₁ , F ₂ , ..., F _N-1 ) the individual delay stages of the polyphase decimator and simultaneously the finite impulse response Filters, the Infinite Impulse Response Filter or the Cascaded Integrator Comb Filter. Filter cascade according to one of Claims 1 to 7, characterized in that the filter length L ~ of the filter path (FP ₁ , FP ₂ ) is determined by the filter length between the one input (E) and an output (A ₁ ; A ₂ ) of the filter path (FP _1; FP ₂₎ serially connected decimating filters (F _0, F _1, F _2, ..., F _{N-1) μ} L filter lengths each corresponding determined according to the following formula:

where R _{ξ is} the decimation factor of the ξ-th polyphase decimator from the input of the filter path (FP ₁ , FP ₂ ). Filter cascade according to Claim 8, characterized in that the polyphase component p _{v of} the vth Polyphase decimator of a filter path (FP ₁ , FP ₂ ) is set so that the vth polyphase decimator at the output (A _v ) of the vth decimating filter (F _v ) after the minimum number of samples at the input (E) of the filter cascade applied input signal (y ₀ (k ₀ )) generates a steady-state sample. Filter cascade according to Claim 9, characterized in that the polyphase component p _{v of} the vth polyphase decimator of a filter path (FP ₁ ; FP ₂ ) iteratively consists of the polyphase component p _{μ of} the μ th polyphase decimator from the input (E) of the filter path (FP ₁ ; FP ₂ ) is determined according to the following formula:

where R _{ξ is} the decimation factor of the ξ-th polyphase decimator from the input of the filter path (FP ₁ , FP ₂ ), L ~ is the filter length of a filter path and MOD {·} is the modulo function.